If the area of the base of a right circular cone is 3850 cm2 and its height is 84 cm, find the slant height of the cone.

Given,


Area of the base of the right circular cone = 3850 cm2


Height of the right circular cone = 84 cm


Let the radius of the cone = r


And the slant height of the cone = l


As,


Area of the base of the cone = 3850 cm2


⇒ πr2 = 3850


⇒ 227 × r2 = 3850


⇒ r2 = 3850 × 722


⇒ r2 = 1225


⇒ r = √1225


Therefore,


r = 35 cm


Now,


length = √h2 + r2


= √(84)2 + (35)2


= √7056 + 1225


= √8281


= 91 cm


So,


The slant height of the given cone is 91 cm.


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